Difference between revisions of "G"
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*G refers to a distinguished point on the secpt256k1 elliptic curve known as the ''generator'' or ''base point''.  
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The symbol ''G'' refers to a distinguished point on the secpt256k1 elliptic curve known as the ''generator'' or ''base'' point.  
  
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Using elliptic curve point addition, one may add G to itself over and over again to form the sequence *G, *G + *G, *G + *G + *G, ... . Eventually every point on the elliptic curve will be generated in this sequence. Although this property is true for any point on the elliptic curve, the particular choice of *G is chosen to be secure against attacks when used in the context of public key cryptography.
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Using elliptic curve point addition, one may add G to itself over and over again to form the sequence  
  
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''G'', ''G'' + ''G'' = 2''G'', ''G'' + ''G'' + ''G'' = 3''G'', ... 
  
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and eventually every point on the elliptic curve will be generated in this sequence.
  
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*G in compressed form is:
 
  
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*G = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798
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In compressed form ''G'' is given by:
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''G'' = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798
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and in uncompressed form is:
 
and in uncompressed form is:
  
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*G = 04 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8
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''G'' = 04 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8
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This particular choice of ''G'' is chosen to be secure against attacks when used in the context of public key cryptography.
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The order *n of *G and the cofactor *h are:
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The order of ''G'' and the cofactor are:
  
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*n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141
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*''n'' = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141
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*h = 01
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*''h'' = 01
  
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The order *n is the number of times *G may be added to itself to get the identity. This generators a subgroup of the group of elliptic curve points, and the fact that the cofactor *h of this subgroup is 1 tells us that this subgroup is the whole group, i.e. *G generates the entrie group.
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The order ''n'' is the number of times ''G'' may be added to itself to get the identity. The cofactor ''h'' = 1 tells us that ''n'' is the order of the group of elliptic curve points, and therefore ''G'' generates the entire group.

Revision as of 15:58, 12 December 2019

The symbol G refers to a distinguished point on the secpt256k1 elliptic curve known as the generator or base point.

Using elliptic curve point addition, one may add G to itself over and over again to form the sequence

G, G + G = 2G, G + G + G = 3G, ...

and eventually every point on the elliptic curve will be generated in this sequence.


In compressed form G is given by:

G = 02 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798

and in uncompressed form is:

G = 04 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798 483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8

This particular choice of G is chosen to be secure against attacks when used in the context of public key cryptography.


The order of G and the cofactor are:

  • n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141
  • h = 01

The order n is the number of times G may be added to itself to get the identity. The cofactor h = 1 tells us that n is the order of the group of elliptic curve points, and therefore G generates the entire group.

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